what are the two integers and which on is the largest?

Question

100 more than the product of of two consecutive even integers is equal to 50 times the largest integer. What is the larger integer? I need help on how to get started with this. Please explain in Steps?

Answer 1

Even integers increase by 2 each time

 

let x = 1st even integer  so x + 2 would equal 2nd even integer

 

translate the words in the problem into an equation

 

100 + x(x + 2) = 50(x + 2)     then distribute

 

100 + x² + 2x = 50x + 100     the 100 on each side will cancel

 

         x² + 2x = 50x           subtract 50x from both sides

 

      x² + 2x - 50x = 0        combine like terms

 

               x² - 48x = 0       factor

 

               x(x - 48) = 0     set each factor equal to 0

 

                x = 0       x - 48 = 0

 

                                      x = 48 

 

so we have 2 answers x = 0 and x = 48

 

when x = 0 then x + 2 = 2    and when x = 48 then x + 2 = 50

 

CHECK

 

x =0 and x + 2 = 2

 

100 + 0(2) = 50(2)

 

100 + 0 = 100

 

       100 = 100√

 

x = 48     x + 2 = 50

 

100 + (48)(50) = 50(50)

 

    100 + 2400 = 2500

 

            2500 = 2500√